Universal formulas for feedback stabilization with respect to Minkowski balls. Malisoff, M. & Sontag, E. Systems Control Lett., 40(4):247–260, 2000.
abstract   bibtex   
This note provides explicit algebraic stabilizing formulas for clf's when controls are restricted to certain Minkowski balls in Euclidean space. Feedbacks of this kind are known to exist by a theorem of Artstein, but the proof of Artstein's theorem is nonconstructive. The formulas are obtained from a general feedback stabilization technique and are used to construct approximation solutions to some stabilization problems.
@ARTICLE{MR1828059,
   AUTHOR       = {M. Malisoff and E.D. Sontag},
   JOURNAL      = {Systems Control Lett.},
   TITLE        = {Universal formulas for feedback stabilization with 
      respect to Minkowski balls},
   YEAR         = {2000},
   OPTMONTH     = {},
   OPTNOTE      = {},
   NUMBER       = {4},
   PAGES        = {247--260},
   VOLUME       = {40},
   KEYWORDS     = {nonlinear control, feedback stabilization, saturation, 
      control-Lyapunov functions},
   PDF          = {../../FTPDIR/minkowski.pdf},
   ABSTRACT     = { This note provides explicit algebraic stabilizing 
      formulas for clf's when controls are restricted to certain Minkowski 
      balls in Euclidean space. Feedbacks of this kind are known to exist 
      by a theorem of Artstein, but the proof of Artstein's theorem is 
      nonconstructive. The formulas are obtained from a general feedback 
      stabilization technique and are used to construct approximation 
      solutions to some stabilization problems. }
}

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